Solve for $x$ and $y$ using elimination. $\begin{align*}2x+4y &= 2 \\ 6x+4y &= -1\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $1$ $\begin{align*}-2x-4y &= -2\\ 6x+4y &= -1\end{align*}$ Add the top and bottom equations. $4x = -3$ Divide both sides by $4$ and reduce as necessary. $x = -\dfrac{3}{4}$ Substitute $-\dfrac{3}{4}$ for $x$ in the top equation. $2( -\dfrac{3}{4})+4y = 2$ $-\dfrac{3}{2}+4y = 2$ $4y = \dfrac{7}{2}$ $y = \dfrac{7}{8}$ The solution is $\enspace x = -\dfrac{3}{4}, \enspace y = \dfrac{7}{8}$.